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Manifesting the Quantum World

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Abstract

In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. Being part of the Scientific Image of the world, the theory concerns the process by which (the physical aspect of) what Sellars called the Manifest Image of the world comes into being. This process consists in the progressive differentiation of an intrinsically undifferentiated entity. By entering into reflexive spatial relations, this entity gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified. If there is a distinctly quantum domain, it is a non-spatial and non-temporal dimension across which the transition from the unity of this entity to the multiplicity of the world takes place. Instead of being constituents of the physical world, subatomic particles, atoms, and molecules are instrumental in its manifestation. These conclusions are based on the following interpretive principle and its more direct consequences: whenever the calculation of probabilities calls for the addition of amplitudes, the distinctions we make between the alternatives lack objective reality. Applied to alternatives involving distinctions between regions of space, this principle implies that, owing to the indefiniteness of positions, the spatiotemporal differentiation of the physical world is incomplete: the existence of a real-valued spatiotemporal background is an unrealistic idealization. This guarantees the existence of observables whose values are real per se, as against “real by virtue of being indicated by the values of observables that are real per se.” Applied to alternatives involving distinctions between things, it implies that, intrinsically, all fundamental particles are numerically identical and thus identifiable with the aforementioned undifferentiated entity.

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Notes

  1. Here Lorentz invariance is assumed to the extent that temporal differentiation and spatial differentiation are mutually implied.

  2. At least this is the case outside of attempts at formulating a quantum theory of gravity.

  3. The following question has been asked by a reviewer (to whom I am grateful for many valuable suggestions): If the wave function does not describe some kind of (holistic) physical reality, how is it possible for experiments to act on the wave function in preparation procedures? The way I see it, the wave function is not something on which experiments can act. Preparation procedures define wave functions, which serve to assign probabilities to the possible outcomes of measurements. On the other hand, nothing stands in the way of positing such a reality, and of thinking of the wave function as a means to describe it by assigning probabilities to the possible outcomes of measurements. We may think of a preparation procedure as acting on such a reality, its effect being what the wave function so describes.

  4. It is often stated that the photon (or the cavity field) stores (or contains) which-way information, but this is misleading at best. Strictly speaking, only an actual state of affairs can contain information. The photon only makes it possible to obtain that information, by detecting it in either of the cavities. The detection of the photon in either cavity creates what the information conveys, namely the fact that the atom went through the corresponding slit.

  5. The experiment discussed by Englert, Scully, and Walter provides a counterexample. As long as the photon is inside the union of the two resonance cavities, the probability of detecting the atom at the screen is given by Rule A, yet the atom cannot be said to have taken a particular slit. This becomes clear when interference is restored, by (i) opening the electro-optical shutters that separate the two cavities and (ii) sorting the detected atoms according as the photosensor situated between the shutters does, or does not, respond.

  6. Chris Fuchs [24, p. 46] knows all about being accused of instrumentalism: “Believe me, you’ve got to stand your ground with these guys when their label guns fly from their holsters! I say this because if one asks ‘Why the quantum?’ in this context, it can only mean that one is being realist about the reasons for one’s instrumentalities. In other words, even if quantum theory is purely a theory for apportioning and structuring degrees of belief, the question of ‘Why the quantum?’ is nonetheless a question of what it is about the actual, real, objective character of the world that compels us to use this framework for reasoning rather than another.”

  7. What is at issue here is the divisibility of a position. Interference fringes have been observed using C\(_{60}\) molecules and a grating with 50-nm-wide slits and a 100-nm period [28]. We do not picture parts of such a molecule as getting separated by many times 100 nm and then reassembling into a ball less than a nanometer across.

  8. Generations of students have been puzzled by the special role that the \(z\) axis plays in descriptions of the stationary states of atomic hydrogen. How does the atom chose this particular axis? The answer, of course, is that it doesn’t. Quantum-mechanical probability assignments are conditional on preparations. In describing the atom’s stationary states we assume that the \(z\) component of its angular momentum has been measured, along with its energy and its total angular momentum.

  9. It is also what makes us conceive of features present in the same place as features of the same object, and to conceive of features present in different places as features of different objects (or of different parts of the same object), so that we are thoroughly baffled by the ability of an indivisible object to pass simultaneously through different slits.

  10. The theorem referred to by Bub is proved in Ref. [39].

  11. In the paper cited, Bell examines a paper by Hepp [42] whose abstract contains the following statement: “In several explicitly soluble models, the measurement leads to macroscopically different ‘pointer positions’ and to a rigorous ‘reduction of the wave packet’ with respect to all local observables.”

  12. Question: If a photon passes a beam splitter, is it not certain to be detected in either of the beams? Answer: What is certain is that the photon will be detected if each beam enters a perfect (100 % percent efficient) detector. Perfect detectors, however, do not exist. A statement involving perfect detectors is equivalent to a conditional statement: the photon will be detected in either beam if a measurement designed to determine the beam taken by the photon is successfully made.

  13. This argument is for illustrative purposes only. \(N_B\) and \(N_L\) are not the (approximately) conserved baryon and lepton numbers.

  14. While neutral particles cannot be inferred directly from particle tracks, they can be inferred indirectly from their interactions with charged particles, on the basis of conservation laws.

  15. Quarks “appear in the phenomena” in a less direct manner than the other standard-model fermions. They appear “as dynamically discontinuous constituent parts of localizable bound systems” [4, p. 262].

  16. According to Falkenburg [4, p. XII], “quantum mechanics and quantum field theory only refer to individual systems due to the ways in which the quantum models of matter and subatomic interactions are linked by semi-classical models to the classical models of subatomic structure and scattering processes. All these links are based on tacit use of a generalized correspondence principle in Bohr’s sense (plus other unifying principles of physics).” This generalized correspondence principle, due to Heisenberg [52], serves as “a semantic principle of continuity which guarantees that the predicates for physical properties such as ‘position’, ‘momentum’, ‘mass’, ‘energy’, etc., can also be defined in the domain of quantum mechanics, and that one may interpret them operationally in accordance with classical measurement methods. It provides a great many inter-theoretical relations, by means of which the formal concepts and models of quantum mechanics can be filled with physical meaning.” [4, p. 191].

  17. It may be asked whether there are particles that are fundamental in this sense. In 1998, the Elementary-Particle Physics Panel of the U.S. National Research Council [54, p. 23] stated that “[t]he question is still open experimentally, but theory and experiment are pointing more than ever before to the possibility that we have discovered the ‘ultimate constituents’.” As recently as 2013, Nicolai [55] affirms that “there is not a shred of a hint so far that would point to an extended structure of the fundamental constituents of matter (quarks, leptons and gauge bosons).”

  18. “The S-matrix...gives transition probabilities which correspond to measurable relative frequencies. But it treats the scattering itself as a black box.... Feynman diagrams...have no literal meaning. They are mere iconic representations of the perturbation expansion of a quantum field theory. They make the calculations easier, but they do not represent individual physical processes.” [4, p. 131–132]

  19. In field theories, the sums over spacetime paths are implicit in the representation of particles by fields, inasmuch as the fields are solutions of the dynamical equations one obtains by summing over spacetime paths.

  20. Those who wish to conceive of space (or spacetime) as a self-existent expanse may do so—on condition that they conceive of it as undifferentiated. What is differentiated is its material “content.” Because this is not differentiated all the way down, the multiplicity inherent in the set-theoretic conception of space (or spacetime) cannot be considered objective. In other words, while substantivalism with regard to an undifferentiated spatiotemporal expanse is defensible, substantivalism with regard to a set-theoretically conceived “continuum” is not.

  21. Sri Aurobindo [62, 63] offers a detailed account of how that ultimate reality comes to take on these essential aspects.

  22. “Hence I am God Almighty,” Schrödinger concludes in the Epilogue to his classic, What is Life? [64], in which he makes explicit reference to Vedanta and the Upanishads.

  23. I venture, however, to say this much: Ever since Leibniz, philosophers have argued that all physical properties are relational or extrinsic, and none are in a fundamental sense non-relational or intrinsic. As was pointed out by Russell [65], this offers the possibility of locating the “categories pertaining to man as a person” [58] in the intrinsic properties of the relata that bear the relational physical properties. It also makes it possible to think of ultimate reality’s essential aspect of quality/delight as the intrinsic nature of \(\fancyscript{E}\). A case can therefore be made for a reversal of metaphysical reductionism: what matters metaphysically is first and foremost what is manifested, or what the manifest image contains; particles are but means to manifest it (and so, presumably, are brains).

  24. Ladyman and Ross [12, pp. 258, 280] concur: “the idea of causation has similar status to those of cohesion, forces, and things. It is a concept that structures the notional worlds of observers.... Appreciating the role of causation in this notional world is crucial to understanding the nature of the special sciences, and the general ways in which they differ from fundamental physics.... There is no justification for the neo-scholastic projection of causation all the way down to fundamental physics and metaphysics.”

  25. One should also bear in mind that quantum theory’s doubly conditional probability assignments do not allow us to formulate causally sufficient conditions for value-indicating events (Sect. 7). While the indicated values of observables (as well as the times at which they are possessed) can be considered objective, causal relations between them cannot.

  26. Why there are \(3 \times 2\) flavors remains something of a mystery.

  27. According to Wilczek [71, p. 164], “Standard model is a grotesquely modest name for one of humankind’s greatest achievements.”

  28. Ladyman and Ross [12, p. 155] ask their readers “to consider whether the main metaphysical idea we propose, of existent structures that are not composed out of more basic entities, is any more obscure or bizarre than the instantiation relation in the theory of universals.” It is not.

  29. Mermin’s thesis [75], according to which “Correlations have physical reality; that which they correlate, does not,” has a different import. Mermin did not claim that there are no correlata, only that they are not part of physical reality. His idea (at the time) was that they belong to a larger reality which includes consciousness, and that the measurement problem only arises in this larger reality.

  30. For an insightful discussion of Plato’s struggle to reconcile unity with multiplicity see Cornford [76]. Twenty-four centuries later, we are still engaged in this struggle, although for the most part we are no longer aware of it.

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Mohrhoff, U. Manifesting the Quantum World. Found Phys 44, 641–677 (2014). https://doi.org/10.1007/s10701-014-9803-3

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